Finite Group DatabasebetaFinite Group Databasebeta| order | 18850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C13 · Schur multiplier (H2) = C5 |
| direct product | C52×C13×D29 |
| unambiguous semidirect product | C29⋊(C2×C52×C13) |
| Fitting, socle, Hall | C52×C13×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C52×C13 |
| Hall | C52×C29 ⋊ C2×C13 |
| Hall | C13×C29 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C13 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C52×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C52×C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9425 |
5200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×C13×#1181, C52×#13094090, C52×D13×D29, … |
| maximal normal subgroup of | C52×C13×#1181, C52×#13094090, C52×D13×D29, … |
| maximal quotient of | C52×C13×Dic29, C2×C52×C13×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18850, 20);